Where can i find huge lists of primes up to as close to 2^128 as possible of SPRP's

[charybdis]

Originally Posted by LarsNet

Charybdis, this is awesome to me, i'm looking for these SPRP's, is there really no place to download them at? Obcoisouly i'm hoping for sizes larger than 64 but it really seems like if i want to do this that i'm going to have to buy the hardware and make them myself

As far as I know no-one has systematically searched for 2-PSPs beyond 2^64. If you want to get to 2^79, you'll probably need lots of fast GPUs, lots of CPUs, and some very efficient code. But as LaurV says, what's the point? The only use I can see would be to extend the search for BPSW pseudoprimes, and this is really only of theoretical interest: even if there is a BPSW pseudoprime below 2^79, it's not like anyone's ever going to come across it by accident. And if we really want to prove primality, APR-CL and ECPP are very quick at this size.

[paulunderwood]

Has anyone done a speed comparison test for a batch of odd numbers < 2^64 between sprp

2, 325, 9375, 28178, 450775, 9780504, 1795265022

and BPSW?[*]

[*] 2-sprp plus strong 2 selfridge strong Lucas chain.

[LarsNet]

Originally Posted by LaurV

What's the purpose of such a list? You can check the primality of any such small N extremely fast, by doing few divisions (very low TF) and then 1, or 2, or few PRP tests. That is because somebody else already did all the work for you, and such tests at this size take microseconds on a modern computer. That would be much faster than reading from a many-GB-sized file.

Mostly it's to test against some prime number testings that i've been working on my own. None of them are better than BPSW, but i found what i think is as good a Miller Rabin test as the deterministic test at the same length (sometimes better) than what they have at wikipedia, but i have some other good ideas and it's mostly an intellectual exercise for me and having these list would help me test what i have come up with, mostly so i don't have to bug those here with my ideas and can work on them on my personal time, does that make sense? :-) I'm looking at the link you posted right now, it looks promising.

I feel like my other post ended up being a waste of time for me and others here's time, and if i have I had these bigger number lists to test against then i could have avoided making the post in the first place since i would have had better numbers to test against and came to the same conclusion ( that my test wasn't better) before hand. That's all really, i just have stuff i'm working on and could use a few gig's worth of numbers to test against. I'm really not opposed to spending money on some equipment that would help me generate these numbers, i just don't know what that equipment would be, right now i just have a laptop which isn't enough to generate the number sizes i'm looking for